Physical and unphysical regimes of self-consistent many-body perturbation theory
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866917675061477376 |
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| author | Van Houcke, K. Kozik, E. Rossi, R. Deng, Y. Werner, F. |
| author_facet | Van Houcke, K. Kozik, E. Rossi, R. Deng, Y. Werner, F. |
| contents | In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order $\mathcal{N}$ and plugged into the Dyson equation, which is then solved for the propagator $G_{\mathcal{N}}\,$. We consider two examples of fermionic models, the Hubbard atom at half filling and its zero space-time dimensional simplified version. First, we show that $G_{\mathcal{N}}\,$ converges when $\mathcal{N}\to\infty$ to a limit $G_\infty\,$, which coincides with the exact physical propagator $G_{\rm exact}\ $ at small enough coupling, while $G_\infty \neq G_{\rm exact}\ $ at strong coupling. This follows from the findings of [Kozik, Ferrero and Georges, PRL 114, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the $G_\infty=G_{\rm exact}\ $ and $G_\infty\neq G_{\rm exact}\ $ regimes thanks to a criterion which does not require the knowledge of $G_{\rm exact}\ $, as proposed in [Rossi et al., PRB 93, 161102(R) (2016)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_04508 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Physical and unphysical regimes of self-consistent many-body perturbation theory Van Houcke, K. Kozik, E. Rossi, R. Deng, Y. Werner, F. Strongly Correlated Electrons In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order $\mathcal{N}$ and plugged into the Dyson equation, which is then solved for the propagator $G_{\mathcal{N}}\,$. We consider two examples of fermionic models, the Hubbard atom at half filling and its zero space-time dimensional simplified version. First, we show that $G_{\mathcal{N}}\,$ converges when $\mathcal{N}\to\infty$ to a limit $G_\infty\,$, which coincides with the exact physical propagator $G_{\rm exact}\ $ at small enough coupling, while $G_\infty \neq G_{\rm exact}\ $ at strong coupling. This follows from the findings of [Kozik, Ferrero and Georges, PRL 114, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the $G_\infty=G_{\rm exact}\ $ and $G_\infty\neq G_{\rm exact}\ $ regimes thanks to a criterion which does not require the knowledge of $G_{\rm exact}\ $, as proposed in [Rossi et al., PRB 93, 161102(R) (2016)]. |
| title | Physical and unphysical regimes of self-consistent many-body perturbation theory |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2102.04508 |